Cummins will be replaced in the Australian XI by debutant Michael Neser, while Steve Smith will skipper the side for the first time since his dismissal as captain in the wake of the 2018 Sandpaper-gate scandal.
The Australian fast bowler was ruled out after coming into close contact with a positive COVID-19 case in an Adelaide restaurant on Tuesday evening.
Cummins was deemed as a close contact by SA Health and will be required to isolate for seven days, ruling him out.
There had been speculation Cummins would need to isolate for 14 days, ruling him out of the third Ashes Test at the MCG, starting on Boxing Day but the isolation period is much shorter.
“We anticipate that he will be available to play in the third Vodafone mens Ashes Test at the MCG in Melbourne,” Cricket Australia said in a statement.
“Cummins is understandably very disappointed not to be able to captain Australia for the day-night Test in Adelaide.”
The late drama is a major twist ahead of the second Test with Australia leading the series 1-0 following a commanding nine-wicket win in Brisbane.
Australia had already lost Josh Hazlewood to a side strain, with Jhye Richardson confirmed to replace him.